Determine the​ vertex, focus, and directrix for the following parabola.

Question

y=5(x-1)^2-10

Answer 1

recall that x^2 = 4py has
vertex at (0,0)
focus at (0,p)
directrix at y = -p
so your parabola,
(x-1)^2 = 1/5 (y+10)
has p = 1/20, and thus
vertex at (1,-10)
focus at (1,-10 + 1/20)
directrix at y = -10 - 1/20